Experimental determination of forces applied by liquid water drops at high drop velocities impacting a glass plate with and without a shallow water layer using wavelet deconvolution

Abstract

Time-dependent forces applied by 2 and 4.5 mm diameter drops of water (with velocities up to terminal velocity) impacting upon a glass plate with or without a water layer (up to 10 mm depth) have been measured using two different approaches, force transduction and wavelet deconvolution. Both approaches are in close agreement for drops falling on dry glass. However, only the wavelet approach is able to measure natural features of the splash on shallow water layers that impart forces to the plate after the initial impact. At relatively high velocities (including terminal velocity) the measured peak force from the initial impact is significantly higher than that predicted by idealised drop shape models and models from Roisman et al. and Marengo et al. Hence empirical formulae are developed for the initial time-dependent impact force from drops falling at (a) different velocities up to and including terminal velocity onto a dry glass surface, (b) terminal velocity onto dry glass or glass with a water layer and (c) different velocities below terminal velocity onto dry glass or glass with a water layer. For drops on dry glass, the empirical formulae are applicable to a glass plate or a composite layered plate with a glass surface, although they apply to other plate thicknesses and are applicable to any plate material with a similar surface roughness and wettability. The measurements also indicate that after the initial impact there can be high level forces when bubbles are entrained in the water layer.

On the measurement and prediction of rainfall noise

“…As mentioned previously, Yu and Hopkins [19] have shown that a thin film of water on the impact surface may affect the impact force. We do not account for this effect here, although we note that in our experience during testing on surfaces at low angles of incidence, the impact surface remained slightly wet such that small puddles sometimes formed close to some droplet impact locations.…”

“…Yu and Hopkins [19] measured the impact velocity for 2 mm diameter and 4.5 mm diameter water droplets falling in air from various heights between 0.41 m and 15 m. They compared their measurements with those predicted using the empirical model of Range and Feuillebois [33] which gives the impact velocity 0 , for a droplet with diameter , density and viscosity falling through air with density from a height as…”

“…This model has therefore been used in the rain noise models of Ballagh [1] (who assumed a cylindrical-hemispherical droplet shape), Guigou-Carter, Villot and Horlaville [10] and Hopkins [11] (who assumed a paraboloidal droplet shape) and Griffin and Ballagh [12] (who consider cylindrical, cylindrical-hemispherical and paraboloidal droplet shapes). Yu and Hopkins [19] have also used this model to derive a force-time history for spherical and ellipsoidal droplet shapes (in addition to their more accurate empirical models). It is important to note that the droplet shapes used in these models do not reflect the actual droplet shape, but have been selected to provide a good match with measurements.…”

“…Yu and Hopkins [19] also conducted a detailed experimental study measuring the force produced by 2 mm and 4.5 mm diameter water droplets impacting onto a horizontal glass surface. To calculate the impact force, they used a wavelet deconvolution method to process the response of the glass to the droplet impact as measured by a number of accelerometers.…”

Effect of Reynolds Number on Impact Force and Collision Process of a Low-Velocity Droplet Colliding with a Wall Carrying an Equal-Mass Deposited Droplet

“…In the study of Ref. (Yu and Hopkins, 2018), an accelerometer array was used to measure the impact force when a droplet impacted on a liquidfilm wall. Their experimental results showed that for the same droplet impacting on different wet walls at the same impact velocity, the impulses of the impact forces may differ considerably.…”